Even as I posted it I wasn’t satisfied with my Mood-O-Meter post from a few days ago. I knew intuitively that in order for the gears to display all possible “moods” the ratio of eye expressions to mouth expressions must be in its simplest form but I couldn’t quite describe mathematically why this was the case. The images below attempt to convey this relationship between the expression ratio and the gear ratio both mathematically and visually.

Essentially, to find how many “moods” will be displayed the numerator is multiplied by the simplified denominator. If the ratio is already in its simplest form, then this is obvious. For the ratio of 6:5, the viewable moods will be 6 x 5 = 30. But in the case of 6:4 (which can be reduced to 3:2), the viewable moods will be 6 x 2 = 12. In the more extreme example a ratio of 4:4, this is reduced to 1:1 so the viewable moods are limited to 4 x 1 = 4.

A few weeks ago I volunteered to lead a make and do session for a staff team building “fun day.” Two nights before the event I started prototyping this “Mood-O-Meter” which actually presented an interesting mathematical problem: what combination of gear teeth and multiples of eye and mouth expressions will display all possible mood options?

For example if I had two 12 tooth gears it wouldn’t matter if I put four eye expressions on one and four mouth expressions on the other because only four expressions out of a possible of sixteen would ever display.

If I printed four expressions on one 12 tooth gear and three on the other this would be even worse as only one mood would be displayed. The other eleven options would always be out of sync.

I settled upon a 18 tooth and 15 tooth with six eye expressions and five mouth expressions respectively to produce 30 individual moods.

My colleagues at Texas Performing Arts cutting out gears to make their Mood-O-Meters. They may have lacked the exuberance of my elementary aged students but when they meshed their gears for the first time they were positively giddy.

I’ve spent perhaps 150 hours working on this in CAD and less than 30 in the studio prototyping. Once all the patterns are printed and stuck to the double thick cereal boxes I think my students will have a shot at building their own in 12 hours of class time.

I finally have a complete design. There has been a lot of back and fourth between CAD and studio: design an element, build a prototype, redesign, tinker, second prototype, sketch, think about it for a while, third prototype. So even though I have yet to build a complete clock I do have some confidence that it will work.

But first a vacation back to the Fatherland to celebrate my Dad’s 70th Birthday!

I had been pondering the best way insert bushings into cardboard for days when it came to me while I was putting on my daughter’s shoes — grommets! A little sanding with 220 grit on the 1/4″ dowel and it runs quite nicely. I’d didn’t have any 1/8″ dowel on hand but to my delight, I found that bamboo skewers are a remarkably consistent 0.005″ less than 1/8″.

The double thickness of Cheerios box may be a bit of challenge to cut for 10-year-olds, but with sharp scissors and some determination I really think they can do it. They’re too young for carpal tunnel syndrome right?